Van Gundy, currently an NBA television analyst for ESPN, has expressed interest in the position and is the third confirmed candidate after Chicago Bulls coach Tom Thibodeau and Golden State Warriors associate head coach Alvin Gentry.
Gentry is the only candidate to have publicly interviewed for the position, according to the report.
The Pelicans fired Monty Williams on May 12 despite New Orleans improving its record in each of the past three seasons and making the playoffs for the first time since the 2010-11 season.
Van Gundy, 53, last coached during the 2006-07 NBA season. He led the Knicks to the 1999 NBA Finals, where the team lost against the San Antonio Spurs, as well as the 2000 Eastern Conference finals, where the team lost to the Indiana Pacers.
On a call with media members earlier this week, Van Gundy declined to discuss the Pelicans job opening.
"I have too much respect for the coaching profession and the sanctity of a job search to publicly speak about any job openings," he said, according to the ESPN report.
"That's really not my style."
The Pelicans lost to Golden State in the first round of the playoffs four games to none.